We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.
|Number of pages||4|
|Journal||Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Apr 1999|
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